Thank you Aniket for your reply. 

I have performed the analysis of the above two cases seven or eight times by now, and I still cannot figure it out why I get a part suspended in one model, and not suspended in the other. As you suggested, I did suppress the joint and then cleared the solution and performed it again, this time I dont get the part hanging in the air. But by the same reasoning, when I apply a joint (an 'empty' one) on to a solution with bonded contacts (and a resulting suspended part), I get a solution that is not suspended anymore. I dont know which solution to believe or where I am going wrong. But in any case, why is that part suspended anyway? If we are saying that bonded contacts act like a 'glue', why does that part hang? Is it because the connection fails?

As for your other recommendation of shared topology, I performed shared topology in spaceclaim for my geometry. However, when I bring it to Ansys and try to mesh, after only a few seconds, an error appears: The mesher can not determine the endpoints for one or more edges.

And:  Mesher failed to mesh topological edges. 

I cannot even generate fixed joints. For my geometry, I would need to generate automatic joints, but the automatic joints that ansys generates are not edge-to-edge joints that I would like. I dont know how to obtain that? Any ideas?